There are many names to the defense mostly centered upon reasonable doubt. But in some cases judges are requested to give even more specific jury instructions.

Lisa Steele has posted Investigating and Presenting an Investigative Omission Defense (Criminal Law Bulletin, Vol. 57, Forthcoming) on SSRN. Here is the abstract:This paper explores defense challenges to the adequacy of police investigations, and investigative lapses as a cause for reasonable doubt. It focuses on case law from Massachusetts, which has four decades of state appellate case law about investigative omission evidence and jury instructions. It talks about the constitutional nature of the defense, how it differs from third-party culprit defenses, and evidence issues that may arise.

The paper also discusses cognitive biases that can affect even well-trained, experienced police investigators and/or prosecutors. Tunnel vision, confirmation bias, and other mental shortcuts can lead to investigative lapses when evidence that the defendant is not the culprit is mentally ignored or downplayed.